Keen 4 Easter eggs
By entering the Pyramid of the Moons and locating a picture of a crescent moon drawn onto the floor, you can make Keen moon. Simply stand on the picture of the crescent moon and wait. Keen normally looks impatient and after a while sits down to read a book, however if you are standing on the moon picture then instead of reading a book Keen will moon the player.
This can only be done once per game, you will need to exit and reload the game to do it again.
The Secret Level
There is a secret level in Keen 4, called the Pyramid of the Forbidden. To reach it, first enter Pyramid of the Moons. At the lowest area are a bunch of Inchworms spread about. You need to gather all 12 of them in one spot. To do this, you must close the bridge on the left and open the door (with the yellow key gem) on the right. When all are gathered, a huge foot materializes (because 12 inches makes one foot). Jump up onto this foot. Keen will exit the level and be carried over to the secret pyramid.
There is also a subtle reference to this in the help section. The description of the Inchworm in The Cast of Characters reads: " ... Watch where you step or they'll be afoot!" This is why the Hints and Cheats sheet says to "Reread the Cast of Characters carefully."
Keen Dreams level loading animation
While not strictly an Easter egg as a patch is required to activate it, the level loading progress bar from Keen Dreams was left behind, unused but fully functional, in Keen 4. Normally it is replaced by the usual finger countdown animation, however this replacement action can be disabled, resulting in the original progress bar being seen instead.
See the 8088MPH blog post for details.
See Keen Dreams style window patches for Keen 4-6 patches that do as described above.